There is a chapel in our diocese that conducts a Latin Mass every Sunday. The diocese stated recently in the diocesan newspaper that the diocese does not condone the Mass. The Mass is celeberated by a priest from a local monastery that is not recognized by the bishop. Can I attend that Mass for my Sunday obligation?
Theoretically speaking, such a Mass could fulfull the Sunday obligation if no licit Mass were available. However, if no such Mass is available, you are dispensed from the Sunday obligation and have no need to try to fulfill it at an illicit Mass.
If the Mass in question is not recognized by your local diocese as a licit Mass, that means that you should not attend. It is a Catholic’s obligation to attend a licit Mass on Sundays and holy days of obligation.